Would you be able to state the issue in more detail?
From where did you get the installation copy of the flash player?
Are you 100% sure that the installation copy of the flash player is genuine?
This is your operating system prompting for the administrator password. This is required by some software that writes to file-system protected locations. If the account you use to log into your computer has administrator permissions, use that account. If it doesn't, you'll need the person who's account has administrator permissions to provide the account password.
Also, Flash Plyaer 10.3.183.29 is very, very old. It is not recommended to use this version on any currently supported mac OS version. Please go to https://get.adobe.com/flashplayer to download the most recent, secrure version.